A full-wave technique is developed for fast analysis of high-frequency planar interconnects and microwave circuits. The proposed methodology is an extension of the adaptive integral method to the objects enclosed in a rectangular box with perfect electrically conducting walls. It can be used for simulation of both shielded and open structures. The only limiting condition for the open circuit analysis is that the substrate is to be electrically thin in the frequency range of interest. The advantage of the proposed method compared to the FFT based techniques adopted in the commercial tools such as Sonnet EM simulator is in the adaptive scheme allowing efficient FFT use for the circuits not fitting onto the FFT grids. The computational time per iteration and memory usage for the solver scale as O(N log N) and O(N) respectively, where N is the number of unknowns in the discrete model. The accuracy and efficiency of the solver is demonstrated through its application to the modeling of a microwave filter.